Problem: Rewrite as a simplified fraction. ${0.69\overline{1} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 691.1111...\\ 100x &= 69.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 622}$ ${x = \dfrac{622}{900}} $ ${x = \dfrac{311}{450}} $